LLM-Guided Dual-Stage Latency Optimization for Closed-Loop 6G V2I Digital Twins

LLM-Guided Dual-Stage Latency Optimization for Closed-Loop 6G V2I Digital Twins

arXiv:2610.22848v1 [cs.NI] 16 Oct 2026

Liu Cao, Member, IEEE, Peide Li, Yuan Yang, Zhaoyu Liu, Lyutianyang Zhang, Member, IEEE, Jinke Ren, Member, IEEE, and Shuguang Cui, Fellow, IEEE Abstract—Wireless Digital Twins (DTs) are emerging as a key enabler for predictive network control in 6G Vehicle-toInfrastructure (V2I) systems. However, closed-loop V2I DTs face two dual-stage communication bottlenecks arising from model parameter exchange for V2I DT reconstruction and multi-service V2I traffic delivery after each reconstruction. This paper proposes a closed-loop dual-stage End-to-End (E2E) latency optimization framework that integrates Compressed Personalized Federated Learning (CPFL) with a unified Large-Language-Model-guided Multi-Agent Reinforcement Learning (LLM-MARL) approach. A CPFL-enabled decision-oriented V2I DT is first constructed by jointly predicting Path Loss (PL) and Quality-of-Experience (QoE)-oriented Key Performance Indicators (KPIs). Then the framework comprises two temporally coupled but latency-wise distinct optimization stages: Stage I minimizes the joint Uplink (UL) and Downlink (DL) E2E transmission latency of compressed shared backbone’s parameters, and Stage II minimizes the service-aware E2E latency of multi-service V2I traffic. As the two stages share aligned agent roles and action space, we develop a unified Semantic-Aware Guidance-Enhanced MultiAgent Proximal Policy Optimization (SAGE-MAPPO) framework, in which the LLM acts as a training-time semantic planner that provides high-level traffic splitting and power allocation guidance to reduce inefficient exploration, while the MARL agents execute feasible low-level actions. Simulation results demonstrate that the proposed framework enables efficient V2I DT reconstruction and significantly reduces both E2E latency for DT reconstruction and multi-service V2I traffic. The proposed SAGE-MAPPO supports cross-stage policy reuse by sequentially solving the two stages within each DT update cycle, which accelerates convergence relative to the existing baselines and facilitates timely DT updates in dynamic V2I scenarios. Index Terms—Digital Twins, Vehicle-to-Infrastructure, Resource Allocation, 6G

I. I NTRODUCTION

W

ITH the rapid evolution toward 6G intelligent transportation systems, Vehicle-to-Infrastructure (V2I) networks are expected to support highly dynamic, latencysensitive, and service-aware communications [1], [2]. In dense urban environments, vehicles experience fast channel fluctuLiu Cao, Peide Li, Yuan Yang, and Zhaoyu Liu are with Electrical and Electronic Engineering Program of both City University of Hong Kong (Dongguan), Dongguan, Guangdong 523808, China and City University of Hong Kong, Hong Kong (e-mail:liu.cao@cityu-dg.edu.cn). Lyutianyang Zhang is with the School of Microelectronics and Communication Engineering, Chongqing University, Chongqing 400044, China (email: zhanglyutianyang@cqu.edu.cn). Jinke Ren and Shuguang Cui are with the School of Science and Engineering, the Shenzhen Future Network of Intelligence Institute, and the Guangdong Provincial Key Laboratory of Future Networks of Intelligence, The Chinese University of Hong Kong (Shenzhen), Shenzhen, Guangdong 518172, China (email: {jinkeren, shuguangcui}@cuhk.edu.cn). (Corresponding author: Lyutianyang Zhang.)

ation, frequent Line-of-Sight (LoS)/Non-LoS (NLoS) transitions, dynamic blockage, and time-varying traffic loads. These characteristics make it difficult for conventional model-based network planning tools to provide accurate and timely guidance for V2I resource management [3], [4]. As a result, wireless Digital Twins (DTs) have emerged as a promising solution for building a synchronized virtual representation of the physical wireless environment, enabling predictive network control and closed-loop optimization [5]. However, constructing a practical V2I DT is generally challenging. First, a DT should provide decision-oriented network states, such as Signal-to-Interference-plus-Noise Ratio (SINR), achievable data rate, Base Station (BS) load, queueing delay, and Quality-of-Experience (QoE)-related Key Performance Indicators (KPIs). These quantities are directly coupled with downstream V2I association and latency-related optimization. Second, the local measurements collected by different vehicles are naturally Non-Independent and Identically Distributed (Non-IID) due to heterogeneous locations, mobility patterns, blockage conditions, and traffic demands [6]. Third, the transmission latency for Federated Learning (FL) is however highly dependent on the link quality of V2I association. Poor V2I association may increase both Uplink (UL) and Downlink (DL) latency, making FL training itself a significant bottleneck for efficient DT reconstruction [7]. In addition to the demand on efficient DT reconstruction, the DT should be able to serve End-to-End (E2E) V2I service. In practical 6G V2I systems, vehicles are able to transmit multiple Vehicle-to-Everything (V2X) types of traffic simultaneously through associated BSs [8]–[10], and the resulting E2E latency consists of both UL and DL components. Optimizing this latency requires the joint control of UL traffic splitting, transmit power, and DL traffic splitting. This problem is difficult because the action space is continuous, the interference and queueing dynamics are coupled, and the latency objective is constrained by the slowest active link path. While MultiAgent Reinforcement Learning (MARL) is a promising tool for solving such dynamic resource allocation problems, however, conventional MARL algorithms often suffer from slow convergence and inefficient exploration in large-scale 6G V2X networks. A. Related Work Recently, wireless DTs have been regarded as a key enabler for 6G network modeling, predictive control, and closedloop optimization [11], [12]. Existing wireless DT studies emphasize on synchronizing physical wireless environments

with digital replicas for online analysis and network control. Different from these studies, our work develops a compressed FL framework to construct a decision-oriented V2I DT. Meanwhile, different from centralized training [13], FL addresses privacy concerns by keeping raw data local [14]–[16] but struggles with data heterogeneity [17], communication bottlenecks [18]–[20], and multi-task complexity. Personalized FL (PFL) mitigates Non-IID effects by retaining client-specific parameters alongside a shared global representation [21]– [23]. Furthermore, gradient compression techniques are widely used to reduce communication overhead [24]. However, most existing FL methods only reduce UL communication overhead and do not explicitly optimize the joint UL and DL parametertransmission latency in each communication round. Traditional Path Loss (PL) prediction methods mainly rely on parameterized empirical models or ray-tracing simulation, which face computational bottlenecks and generalization limits in complex 3D urban environments [25], [26]. Consequently, data-driven approaches using deep neural networks, such as convolutional neural networks (CNNs) and graph neural networks (GNNs), have become the mainstream solutions for radio map construction by learning non-linear mappings between environmental features and signal fading [27], [28]. However, most existing models treat environmental inputs as static binary masks and lack explicit modeling of geometric relationships, such as LoS and NLoS propagation paths. While accurate PL mapping is fundamental, network operations depend directly on KPIs, such as throughput, queueing delay, load, and fairness. Prior data-driven KPI prediction methods [29] often separate radio map construction from multi-BS association decisions, neglecting the non-linear queueing effects and load-coupling dynamics induced by traffic distribution. Multi-Task Learning (MTL) provides a natural framework to jointly optimize linklevel PL and user-level KPIs by sharing feature representations [30]. In contrast, our work jointly learns PL and KPIrelated states, including SINR, data rate, Micro-BS (MBS) load, queueing delay, and QoE-related metrics. Therefore, the reconstructed DT can directly support V2I association and latency optimization. Meanwhile, traditional hard association strategies, such as Max-SINR, frequently cause severe load imbalance in multi-BS networks [31]. To alleviate this issue, soft association instead distributes a vehicle’s traffic over multiple MBSs using normalized rate- or utility-proportional weights whose sum is one [32], [33]. However, in dense urban V2I environments, instantaneous channel quality alone is insufficient because high-rate links may still suffer from unstable NLoS blockage or severe queueing congestion. MARL has been widely adopted for wireless resource allocation because it can learn distributed policies under coupled interference, traffic, and queueing dynamics [34], [35]. Nevertheless, standard MARL often requires extensive exploration when the joint action space includes traffic splitting, power control, and multi-BS scheduling. Recently, Large Language Models (LLMs) have been used as high-level reasoning modules for wireless resource allocation [36]. However, directly using an LLM as a low-level controller is computationally

expensive and may violate strict feasibility constraints. In this work, the LLM is not used to directly output final control decisions. Instead, it provides semantic guidance and soft policy priors for a unified MARL framework, helping the MARL agents identify overloaded MBSs, unreliable links, and preferred traffic splitting directions.

B. Motivation and Contributions To address these challenges, we propose a closed-loop framework that integrates periodic V2I DT reconstruction with a unified LLM-guided MARL framework to solve the dualstage E2E latency optimization problems, where the joint E2E UL and DL transmission latency and V2X service-aware traffic are iteratively optimized respectively. A key feature of our design is that the LLM acts as a semantic planner that summarizes global network states and provides high-level guidance, such as identifying overloaded BSs, unreliable links, and preferred traffic splitting tendencies. The final feasible actions are still executed by the proposed MARL agents and optimized through reward feedback. This design preserves the adaptability and constraint awareness of MARL while using LLM-based semantic reasoning to reduce redundant exploration and accelerate convergence. The main contributions are summarized as follows: We develop a Compressed Personalized FL (CPFL)enabled DL V2I DT, augmented with online UL channel measurements. The resulting hybrid state provides a consistent decision basis for bidirectional V2I transmission control. Meanwhile, we design a joint geometry and KPIaware V2I association strategy assisted by the reconstructed DT for downstream E2E multi-path transmission architecture. • We formulate dual E2E latency optimization problems in which transmission structures occur in a unified manner in each closed-loop DT-update cycle. Both structures share the same agent roles and action space where each vehicle optimizes the UL traffic splitting and transmit power, while the edge server controller optimizes the DL traffic splitting. • We develop a unified Semantic-Aware GuidanceEnhanced Multi-Agent Proximal Policy Optimization (SAGE-MAPPO) framework to solve both optimization problems. The LLM provides training-time semantic guidance, helping MARL agents reduce inefficient exploration. By sharing the same architecture across both E2E latency optimization problems, the proposed method enables cross-problem policy reuse and achieves faster convergence than training-independent MARL controllers. •

The rest of this paper is organized as follows. Sec. II introduces the system model and the closed-loop CPFL-enabled V2I DT reconstruction framework. Sec. III presents the unified LLM-MARL framework. Sec. IV provides the performance evaluation of DT reconstruction, convergence behavior, and E2E latency optimization. Finally, Sec. V concludes this paper.

Periodic Efficient V2I DT Reconstruction via CPFL

DT-Assisted V2I Association

Efficient E2E Multi-path Transmission Architecture via Unified LLM-MARL MBS b

Vehicle Agent i Current V2I DT Ends Uplink Transmission Downlink Transmission

Radio links

Backhaul links

MBS b+1

Edge Server Agent

During CPFL Training: t E2E Shared Backbone Para. Transmission During Reconstructed DL V2I DT:

2) DT KPI Prediction: The second task is DT KPI prediction. The DT KPI vector of vehicle i is constructed as  DL  DL yiKPI = {γb,i }b∈B , {Rb,i }b∈B , {Lb }b∈B , {Db }b∈B , J , (2) DL DL where γb,i and Rb,i are the measured SINR and DL data rate at vehicle i from MBS b, respectively. Lb is the data load of MBS b given the association weight wi,b between vehicle i and MBS b, which is given by X Lb = wi,b . (3)

Multi-Service of V2X Traffic Transmission

Fig. 1: Closed-Loop 6G V2I DT-Assisted Dual-Stage E2E Latency Optimization Framework. II. D UAL -S TAGE O PTIMIZATION P ROBLEM F ORMULATION Let us consider a 6G V2X network consisting of a set of vehicles I = {1, . . . , I}, a set of MBSs B = {1, . . . , B}, and an edge server. Each vehicle collects local wireless measurements and environmental observations to collaboratively reconstruct a DL V2I DT. Since the wireless environment is time-varying due to vehicle mobility, dynamic blockage, channel fluctuation, and traffic-load variation, the V2I DT is periodically updated. Let K = {1, . . . , K} denote the set of DT update indices, where each k ∈ K corresponds to one (k) DT reconstruction cycle. Let Di denote the local dataset measured at vehicle i during the k-th DT update cycle. To reduce communication overhead while preserving personalization, each vehicle employs a CPFL model consisting of (k) a global shared backbone w(k) and a local head vi . The shared backbone captures common wireless propagation and traffic patterns, while the personalized head captures the DL channel, blockage, and load characteristics. During the CPFL training, only the compressed shared backbone parameters are transmitted between the server and vehicles, while the local head parameters are not transmitted. We assume that each (k) vehicle i can obtain its DL local dataset Di through practical V2I measurements from the MBS set B, including link-quality, traffic-load, and environmental observations. The raw measured data remain local and are not uploaded during CPFL training. A. Multi-task DT Prediction The proposed CPFL model performs two coupled DT tasks: 1) DT PL Prediction: The first task of the CPFL-enabled DT is PL prediction. The PL from MBS b to vehicle i is given by P Lb,i , which can be obtained based on the measured received power at vehicle i and the transmit power obtained from the control information in Physical Downlink Control Channel (PDCCH). The PL prediction head learns the nonlinear mapping fiPL from local DT features to the measured PL vector: biPL = fiPL (zi ; w, vi ) ≈ {P Lb,i (xloc , yloc )}b∈B , y

(1)

biPL is the PL vector predicted by vehicle i. zi denotes where y

the geometry-enhanced local DT feature vector observed by vehicle i at its location (xloc , yloc ), which is constructed as zi = [xloc , yloc , building mask, road mask, vehicle mask, relative MBS distance features, LoS confidence features].

i∈I

Note that wi,b depends on the V2I association strategy to be determined. Db is the expected queueing delay of MBS b that follows the M/M/1 queueing model, which is expressed as 1 Db = , (4) µb − λb where µb is the service rate and λb is the traffic arrival rate at MBS b. J is the Jain’s fairness index among all vehicles, which is expressed as
P DL 2 i∈I Ri P , (5) J= |I| i∈I (RiDL )2 where the DL data rate at vehicle i is given by X DL RiDL = wb,i Rb,i ,

(6)

b∈Bc DL where Rb,i is the DL data rate at vehicle i from MBS b. bi from local DT The KPI prediction head learns the mapping y features to the measured DT KPI vector:
biKPI = fiKPI zi ; w, viKPI ≈ yiKPI , y (7)

biKPI is the KPI vector predicted by vehicle i. where y We evaluate the DL performance between vehicle i and each MBS b in terms of the predicted KPI vector. Let Vi,b denote a KPI-aware effective V2I metric between vehicle i and MBS b that jointly reflects the link-level and system-level quality, which is given by Vi,b = ω T gi,b (b yiKPI ),

(8)

where gi,b (b yiKPI ) is the normalized KPI vector as a function biKPI , which is expressed as of the predicted KPI vector y h iT DL e DL eb , 1 − D e b , Je , gi,b (b yiKPI ) = γ eb,i , Rb,i , 1 − L (9) and ω is the corresponding KPI-weight vector satisfying T

ω = [ω1 , ω2 , ω3 , ω4 , ω5 ] ,

ωk ≥ 0,

5 X

ωk = 1.

(10)

k=1

It should be noted that the proposed CPFL model reconstructs a downlink-oriented V2I DT that determines the association and supplies the DL-side decision states. It does not predict the action-dependent instantaneous UL metrics which are updated online. B. DL V2I DT Reconstruction The general training procedures for V2I DT reconstruction are summarized as follows:

1) DT-assisted V2I Association: A typical V2I association strategy is based on the highest predicted SINR or the highest achievable data rate, which is however insufficient in dense urban scenarios: a radio link with high SINR and data rate may still suffer from unstable NLoS impacts due to buildings, vehicles, and street-canyon blockage, leading to unreliable service, unbalanced BS load, and increased queueing delay. To address these issues, we propose a DT-assisted NLoS-aware V2I association strategy that combines the predicted data rate with explicit geometric visibility information zi . We define a (k) continuous LoS confidence ψi,b using the Bresenham’s line algorithm [37]. Specifically, the line segment between MBS b and vehicle i during kth DT is discretized into grid cells. Let (k) Ntot (i, b) be the number of grid cells on this line segment and (k) Nblock (i, b) be the number of grid cells occupied by blockage regions. Then, the LoS confidence is defined as ! (k) Nblock (i, b) (k) , (11) ψi,b = max 0, 1 − η · (k) Ntot (i, b) where η is an adjustment coefficient. ψi → 1 for pure LoS, while ψi → 0 for deep occlusion, thereby serving as a physically meaningful geometric prior. Then the proposed V2I association weight over all candidate MBSs is (k)

(12)

b∈B

where Vi,b is calculated in Eq. (8), β ∈ [0, 1] is the sensitivity weight to balance the KPI-aware performance and the linklevel reliability. After obtaining the soft association weights wi,b over all candidate MBSs, the vehicle i associate with (k) (k) the Ks MBSs with the top-Ks largest weights wi,b . Let Bi denote the associated top Ks MBSs for vehicle i in the k ≥ 1 DT update. The final association weight is then re-normalized within the selected top-Ks MBS set:  (k) w  (k)   P i,b , b ∈ Bi ,  (k) (k) w i,b (13) wi,b =   b∈Bi(k)   (k) 0, b∈ / Bi , P where the V2I association weights satisfy b∈Bi wi,b = 1, ∀i. Note that for the initial V2I association k = 0, each vehicle selects the highest-SINR MBS used for the UL and DL transmission during CPFL training: (0)

else Extract vehicle location xi ; for each MBS b ∈ B do (k) Compute the LoS confidence ψi,b according to Eq. (11); Compute the DT-assisted V2I association weights according to Eq. (12) and Eq. (13); (k) Select the associated top-Ks MBS set Bi ; (k)

(k)

(Vi,b )β (ψi,b )1−β (k) , wi,b = P (k) (k) (Vi,b )β (ψi,b )1−β

Bi

Algorithm 1: DT-Assisted NLoS-Aware V2I Association Strategy Input: Vehicle set I, MBS set B, DT update index k, (k) predicted KPI-aware V2I metric {Vi,b }, DL DL SINR {γb,i }, geometric map Zgeom , LoS adjustment coefficient η, sensitivity weight β, number of selected MBSs Ks (k) Output: Association sets {Bi }i∈I and final (k) association matrix W (k) = {wi,b } Initialize W (k) = 0|I|×|B| ; for each vehicle i ∈ I do if k = 0 then (0) Select the initial MBS set Bi according to Eq. (14);

DL = argmax {γb,i }b∈B .

(14)

b (k)

That is, the corresponding association weight wi,b = 1. The entire DT-assisted NLoS-Aware V2I association procedure is described by Algorithm 1. 2) CPFL Model Update: In the proposed CPFL-enabled V2I DT framework, two prediction tasks of PL and KPI are designed to share the same global backbone while being predicted by separate task heads. This design is motivated by the fundamental differences between PL and KPI in terms of

(k)

return {Bi }i∈I , W (k) = {wi,b } physical mechanisms, statistical characteristics, and decisionmaking roles: PL primarily reflects the link-layer channel attenuation, which is influenced by geometric blockages, LoS/NLoS conditions, and relative positions of MBSs, exhibiting local variability and strong interpretability. In contrast, KPI represents the system-level performance, which depends on the scheduled V2I association, interference coupling, traffic dynamics, and queueing, exhibiting highly nonlinear and globally coupled behavior. Modeling them separately allows the PL head to focus on capturing the link-level characteristics, while the KPI head leverages the shared backbone features and PL outputs to effectively predict system-level metrics. Based on the above two DT reconstruction tasks, the CPFL loss objective is formulated as min (k)

w(k) ,{vi

X 1 }i∈I i∈I |I|

(k)

Li (w(k) , vi ),

(15)

where the local multi-task loss of vehicle i is KPI Li = αLPL , (16) i + (1 − α)Li P 2 1 biPL (d) − yiPL (d) 2 and where LPL = y (k) (k) i d∈Di |Di | P 2 1 biKPI (d) − yiKPI (d) 2 are the PL y LKPI = (k) (k) i d∈D |Di

|

i

and KPI prediction loss of vehicle i, respectively. α ∈ [0, 1] is the multi-task balancing weight between the two prediction loss. Then each vehicle computes its local update (k)

(k)

∆i (t) = wi (t) − w(k) (t), (k)

(17)

where wi (t) is the locally updated backbone during the kth DT update. To improve the communication efficiency, we

propose to compress such update before transmission via the joint sparsification and quantization function:   e (k) (t) = Q ∆(k) (t) , ∆ (18) i i where the Q function first selects the top ps % ratio of entries in (k) ∆i (t) with the largest magnitudes, while setting all remaining entries to zero. Then the Q function quantizes the retained entries into a nq -bit representation. This function ensures that only the changes are transmitted, effectively reducing the communication cost. After receiving all compressed shared backbone parameters from participating vehicles, the edge server dequantizes the values to approximate the original magnitudes, and aggregates them by weight-averaging: 1 X e (k) ∆i (t). (19) w(k) (t + 1) = w(k) (t) + |I| i∈I

We then prove that our proposed CPFL converges to a stationary global model with the non-convex loss. For notational convenience, we omit the index of DT index k and unless otherwise stated. To derive the expected convergence rate, we make following assumptions: • Assumption 1: We assume that fi (w, v) is differentiable and L-smooth for any vehicle i, i.e., ∥∇fi (x)−∇fi (y)∥ ≤ L∥x − y∥, where x = (w, v), y = (w′ , v′ ). Equivalently, fi (y) ≤ fi (x) + ⟨∇fi (x), y − x⟩ + L2 ∥y − x∥2 . • Assumption 2: We assume that the stochastic gradient gi (x; Di ) is unbiased with bounded variance given the local  dataset Di at vehicle i, i.e., E[gi (x; Di )] = ∇fi (x), E ∥gi (x; Di ) − ∇fi (x)∥2 ≤ σ 2 . ∗ • Assumption 3: We assume that there exists F such that F (x) ≥ F ∗ for all x. • Assumption 4: We assume bounded local data heterogeneity where backbone satP|I| the gradient of shared 2 1 isfies |I| i ∥∇w fi (x) − ∇w F (x)∥ ≤ γ 2 , where P|I| 1 ∇w F (x) = |I| i=1 ∇w fi (x). • Assumption 5: For the compression operator Q(·), we have E∥Q(∆i (t)) − ∆i (t)∥2 ≤ (1 − ω)∥∆i (t)∥2 , 0 < ω ≤ 1, where ω is the compression ratio. Lemma 1. Under Assumptions 1 and 2, if the step sizes satisfy ηw , ηv ≤ L1 , then we have   1 2 t,e
fi xt,e+1 ≤f x − ηw ∇w fi (xt,e i i i i ) 2  L
2 2 + ηv ∇v fi (xt,e ) + ηw + ηv2 σ 2 , i 2 (20) t,e t,e t,e where xi ≜ (wi , vi ). Proof: See Appendix A. Lemma 2. Under Assumptions 2 and 4, there exists a constant C > 0 that holds I i
1 X h t,E 2 2 E wi − w t ≤ C ηw E 2 σ2 + γ 2 . I i=1

Proof: See Appendix B.

(21)

Theorem 1. Under Assumptions 1-4, suppose the step sizes c satisfy ηw ≤ LE and ηv ≤ Lc for a constant c ∈ (0, 1). Define the mixed stationarity measure as I

G t,e ≜ ∇w F wt , {vt }

2

+

2 1X . (22) ∇vi fi xt,e i I i=1

Then, after T communication rounds with E local steps per round, we have
  T −1 E−1 1 X X  t,e  4 F 0 − F ⋆ 1 1 + E G ≤ T E t=0 e=0 ET ηw ηv + C1 L(ηw + ηv )σ 2 + C2 Lηw E 2 γ 2 + C3 L(1 − ω)ηw E 2 (σ 2 + γ 2 ), (23)
where F 0 = F w0 , v0 and C1 , C2 , C3 are positive constants. Proof: See Appendix C. 3) Compressed Shared Backbone Transmission: To further improve the shared backbone transmission efficiency in the UL and DL, we propose to optimize the UL traffic splitting ratio, the transmit power of each vehicle, and the DL traffic splitting ratio of its associated MBSs1 in each communication round t during the kth DT update. Let ΞDL(k) (t) denote the number of DL bits required to deliver the global shared backbone’s DL(k) parameters from the edge server to each vehicle, and ρb,i (t) denote the traffic splitting ratio from MBS b to vehicle i. Let UL(k) Ξi (t) denote the number of UL bits required for vehicle i UL(k) to upload its compressed shared backbone’s update, ρi,b (t) denote the UL traffic splitting ratio from vehicle i to MBS (k) UL(k) b ∈ Bi (t), and Pi,b (t) denote the corresponding UL transmit power. It is worth noting that ΞDL(k) (t) is identical for all vehicles, since the server broadcasts the same global UL(k) parameters. In contrast, Ξi (t) is vehicle-specific, because each vehicle may generate a different compressed local update depending on the local measured data. Then the UL SINR from vehicle i to MBS b is UL(k)

UL(k) γi,b (t) =

Pi,b P i′ ̸=i

UL(k)

(t)hi,b

(t)

UL(k) UL(k) Pi′ ,b (t)hi′ ,b (t) + σ 2

,

(24)

UL(k)

where the channel gain hi,b (t) is assumed to be constant during the communication round t, and σ is the noise power. Thus the achievable UL data rate is   UL(k) UL(k) UL(k) Ri,b (t) = Bi,b (t) log2 1 + γi,b (t) . (25) The UL transmission latency over the UL path includes the UL radio link latency between vehicle i and MBS b and the UL backhaul latency between MBS b and the edge server, which is given by UL(k) UL(k) UL(k) UL(k) ρi,b (t)Ξi (t) ρi,b (t)Ξi (t) UL(k) Ti,b (t) = + , UL(k) UL(k) Ri,b (t) ci,b (t)

(26)

1 The MBS DL transmit power is fixed and is included in the DT-based DL rate prediction; it is therefore not treated as an optimization variable.

UL(k)

where ci,b (t) is the UL Guaranteed Bit Rate (GBR) between the MBS b and the edge server. Similarly, the DL transmission latency over the DL path (b, i) is DL(k)

DL(k)

Tb,i

ρb,i

(t) =

(t)ΞDL(k) (t)

DL(k)

Rb,i

DL(k)

+

ρb,i

(t)ΞDL(k) (t)

DL(k)

(t)

cb,i

, (27)

(t)

DL(k)

where Ri,b (t) is the DL data rate from MBS b to vehicle i DL(k) based on the predicted DT, cb,i (t) is the DL GBR between the edge server and the MBS b. Therefore, the joint UL and DL shared backbone transmission latency between the vehicle i and the edge server via the MBS b is (k)

UL(k)

Li,b (t) = Ti,b

DL(k)

(t) + Tb,i

(t).

(28)

Then the corresponding transmission latency between the vehicle i and the edge server is the maximum latency among all (k) associated paths over Bi , given by (k)

(k)

Li (t) = max Li,b (t).

(29)

(k)

b∈Bi

Our objective is to minimize the joint UL and DL shared backbone transmission latency in each communication round t during the kth DT update, which is formulated as Problem 1 (Stage-I DT-Update Model-Exchange Latency Optimization). (k)

min UL(k) UL(k) DL(k) ρi,b (t), Pi,b (t), ρb,i (t)

max Li (t)

(30)

i∈I

UL(k)

s.t. C1 : 0 ≤ ρi,b (t) ≤ 1, ∀i ∈ I, b ∈ Bi (t), X UL(k) C2 : ρi,b (t) = 1, ∀i ∈ I,

(30a) (30b)

b∈Bi (t) UL(k)

C3 : 0 ≤ Pi,b C4 :

UL(k)

X (k)

(t) ≤ Pimax ,

Pi,b

(k)

∀i ∈ I, b ∈ Bi (t), (30c)

(t) ≤ Pimax ,

∀i ∈ I,

(30d)

Algorithm 2: Efficient V2I DT Reconstruction Input: Vehicle set I, V2I association sets (k) {Bi (t)}i∈I , communication rounds T , local epochs E Output: Trained global shared backbone w(k) and personalized heads {vi (k)}i∈I Initialize global shared backbone w and personalized heads {vi }i∈I ; for Each DT reconstruction k = 0, 1, . . . , K − 1 do (k) Build V2I association sets {Bi }i∈I using Algorithm 1; for Each communication round t = 0, 1, . . . , T − 1 do for each vehicle i ∈ I in parallel do Set local shared backbone wit,0 ← wt and personalized head vit,0 ← vit ; for Each local epoch e = 0, 1, . . . , E − 1 do Update wit,e+1 and vit,e+1 by minimizing the local multi-task loss Li in Eq. (16); Set wit+1 ← wit,E and vit+1 ← vit,E ; Compute the local shared backbone update in Eq. (17); Compress the shared backbone update in Eq. (18); e (k) (t) through associated Split and upload ∆ i UL(k) UL(k) MBSs in terms of {ρi,b (t), Pi,b (t)} in Problem 1; (k)

e (t) in Eq. (19); Aggregate the uploaded ∆ i (k) t+1 Split and download w through Bi (t) in DL(k) terms of ρb,i (t) in Problem 1; (k)

return w(k) , {vi }i∈I (k)

C. E2E Multi-Service of Traffic Transmission Once the DT is updated, each vehicle i further transmits Q = {1, . . . , Q} types of traffic2 to the edge server and the

traffic of each type is split via the associated MBS set Bi . To minimize the service-level E2E UL and DL latency in the whole system where each vehicle i optimizes the UL traffic splitting ratio and the UL transmit power over the associated MBSs, while the edge server optimizes the DL traffic splitting ratio3 . We consider block-fading channels where the UL UL(k) DL(k) channel hi,b (m) and the DL channel hb,i (m) between vehicle i and MBS b are assumed to be constant within a block and vary independently across M = {1, . . . , M } blocks in the kth DT update. Accordingly, joint decisions are made at the beginning of each block and kept fixed for the whole block. In each block m ∈ M, suppose the number of arrived packets of traffic type q at the vehicle i ini block m is a random h (k) (k) (k) variable λi,q (m) with mean E λi,q (m) = λ̄i,q . Each packet of traffic type q has a fixed size of Mq bits, and all packets with (k) the same type share the same size. Meanwhile, let Wi,q (m) denote the number of queueing packets of htype q at vehicle i at i (k) the beginning of block m with the mean E Wi,q (m) = W̄i,q .

2 According to the 3GPP standard [8], [9], the V2X traffic service types includes broadcast, unicast and groupcast.

3 The DL transmit power of the MBS is determined by the reconstructed DT, which is thereby not optimized here.

b∈Bi

(t)

DL(k)

(k)

C5 : 0 ≤ ρb,i (t) ≤ 1, ∀i ∈ I, b ∈ Bi (t), (30e) X DL(k) C6 : ρb,i (t) = 1, ∀i ∈ I, (30f) (k)

b∈Bi

C7 :

(t)

(k) Li (t) ≤ Lmax CSB ,

∀i ∈ I,

(30g)

where constraints C1-C2 and C5-C6 ensure that each vehicle splits its UL and DL shared backbone’s update among its associated MBSs. C3-C4 impose the UL transmit-power budget of each vehicle. C7 defines the shared backbone’s transmission latency budget for a communication round. Algorithm 2 summarizes the proposed V2I DT reconstruction method. In the following, we formulate the second problem to form the closed-loop perspective.

UL(k)

Let Pi,b (m) denote the corresponding UL transmit power. The UL SINR from vehicle i to MBS b is UL(k)

UL(k) γi,b (m) =

Pi,b P i′ ̸=i

UL(k)

(m)hi,b

(m)

UL(k) UL(k) Pi′ ,b (m)hi′ ,b (m) + σ 2

,

(31)

UL(k)

Ri,b

UL(k)

(m) = Bi,b

(m) log2

 UL(k) 1 + γi,b (m) .

C2 : (32)

UL(k) UL(k) UL(k) αi,b,q (m) λi,q (m) + Wi,q (m) Mq UL(k) Ti,b,q (m) = UL(k) Ri,b (m)
UL(k) UL(k) UL(k) αi,b,q (m) λi,q (m) + Wi,q (m) Mq UL(k)

,

DL(k) DL(k) DL(k) αb,i,q (m) λi,q (m) + Wi,q (m) Mq DL(k) Tb,i,q (m) = DL(k) Rb,i (m)
DL(k) DL(k) DL αb,i,q (m) λi,q (m) + Wi,q (m) Mq + . DL(k) cb,i,q (m) (34) Thus, the joint E2E UL and DL latency for traffic type q between vehicle i and the edge server via MBS b during the block m is (35)

Then the corresponding transmission latency for traffic type q between vehicle i and the edge server is the maximum latency (k) among all associated paths over Bi , given by (k)

(k)

Li,q (m) = max Li,b,q (m). (k) b∈Bi

UL(k)

C3 : 0 ≤ Pi,b C4 :

X

∀i ∈ I, q ∈ Q,

(m) ≤ Pimax ,

UL(k)

Pi,b

(37b)

(m) ≤ Pimax ,

(k)

∀i ∈ I, b ∈ Bi , (37c) ∀i ∈ I,

(37d)

(k) b∈Bi

DL(k)

C5 : 0 ≤ αb,i,q (m) ≤ 1, X

(k)

∀i ∈ I, b ∈ Bi , q ∈ Q, (37e)

DL(k)

αb,i,q (m) = 1, (k)

Quality-of-Service (QoS) flow characteristics of service type q. Similarly, the DL transmission latency for traffic type q over the same path is

DL(k)

UL(k)

αi,b,q (m) = 1,

C7 : max Li,b,q (m) ≤ Lmax , q

where cUL i,b,q (m) follows the distribution of the corresponding

UL(k)

X

(k)

∀i ∈ I, b ∈ Bi , q ∈ Q, (37a)

∀i ∈ I, q ∈ Q,

(37f)

∀q ∈ Q,

(37g)

(k) b∈Bi

(33)

(k)

DL(k)

(m), αi,b,q (m) i∈I q∈Q

(k) b∈Bi

C6 :

ci,b,q (m)

Li,b,q (m) = Ti,b,q (m) + Tb,i,q (m).

UL(k)

UL(k)

We denote the UL traffic splitting ratio of type q traffic from UL(k) vehicle i to MBS b as αi,b,q (m), ∀i ∈ I, ∀q ∈ Q. Therefore, the UL transmission latency for traffic type q, including the radio link latency from vehicle i to MBS b and the backhaul latency from MBS b to the edge server is

+

UL(k)

αi,b,q (m), Pi,b

s.t. C1 : 0 ≤ αi,b,q (m) ≤ 1,

and the corresponding achievable UL data rate is 

Problem 2 (Stage-II Service-Aware Communication Latency Optimization). X X (k) Li,q (m) (37) min

(36)

Our objective is to minimize the joint E2E UL and DL latency per block of all vehicles with all traffic types. Accordingly, we formulate the second optimization problem as follows:

(k) b∈Bi

in C7 is the latency budget of type q. where Lmax q Remark 1. Problems 1 and 2 correspond to two distinct but temporally coupled stages within each DT-update cycle: Problem 1 is executed during the DT reconstruction to minimize the joint UL and DL latency of the global model exchange in each communication round; Problem 2 is executed after DT reconstruction and minimizes the aggregated service-aware joint UL and DL latency in each transmission block, subject to service-specific latency budgets. The two problems are operationally decoupled by their execution order and timescales and are solved sequentially. However, they share the same agent roles and structurally aligned action components: vehicle agents determine UL traffic splitting and UL power allocation, while the edge server’s agent determines DL traffic splitting. Meanwhile, the multi-service types q ∈ Q introduced in Problem 2 corresponds to the global model as the single service type (|Q|=1). Therefore, their action spaces are aligned but not identical, which enable cross-problem policy initialization without merging the two objectives. III. U NIFIED SAGE-MAPPO F RAMEWORK FOR C LOSED -L OOP D UAL O PTIMIZATION P ROBLEMS To solve Problems 1 and 2 in a unified manner, we employ the same LLM-guided MARL architecture, implemented by a SAGE-MAPPO framework. The key idea is that Problems 1 and 2 share the same agent roles and highly consistent control dimensions: the vehicle agents optimize UL traffic splitting and transmit power allocation, while the edge server optimizes DL traffic splitting. Therefore, instead of designing two separate MARL solvers, we design a unified LLM-MARL architecture and instantiate it with problem-dependent state semantics and reward functions. In particular, Problem 1 corresponds to the

High-Level Semantic Planner 2) Environment Translator �

(� ,� )

=� �

(� ,� )

1) Environment Summary Natural language summary of � (� ,� ) Aggregation of environment information for Problem � during kth DT update

V2I Transmission Environment Context �

• “You are an expert trajectory evaluator for 6G V2X routing and power control…… then give a counterfactual recommendation that would reduce congestion or deadline risk……” • “input”:”…… Candidate-link quality:{link_quality}……” • “output”:”…… Required JSON fields: { …… "constraint_tags": ["deadline", "congestion", "power", "routing"]……}”

5) Quantitave Semantic Action Guidance

4) SAGE-Planner ��

(� ,� )

= �(� ���) �

Quantitave Action Guidance

LLM ouput: Semantic Action Guidance

(� ,� )

LLM Backbone

Qwen3.5-9B LLM output: Other Semantic information

v_low

0.00

Low

0.25

Mid

0.50

High

0.75

v_high

1.00

Agent V0 (Edge Server for DL): (� ,� ) �0

Semantic Mapper

Agent V1 (Vehicle 1 for UL): (� ,� )

�1

...

Global State �

(� ,� )

3) Structural Prompt � (� ,� )

Agent VI (Vehicle I for UL): (� ,� )

��

Unified MAPPO Optimization Unified SAGE-Assisted Latency(� ) Driven Reward �� ���−�

�1

Agent VI (Vehicle I for UL)

(� ,� )

��

Semantic-Alignment Reward

(� ,� )

1 for UL) Local(Vehicle Observation

...

Quadratic Latency Penalty

(� ,� )

�0

Agent V1

(� ,� )

�1

Low Latency Reward

Local Action

Agent V0 (Edge Server for DL)

(� ,� ) �0

Latency-Driven Reward Components

Low-Level Action Excuation

Agent Set A

Local Observation

Centralized Critic � (� ,� )

(� ,� )

��

MAPPO Update in Algorithm 3

Fig. 2: Overall Framework of Unified SAGE-MAPPO. efficient shared backbone’s transmission during DT reconstruction, whereas Problem 2 corresponds to the service-aware E2E joint UL and DL latency optimization. 1) Unified SAGE-MAPPO Components: The fundamental components of SAGE-MAPPO are described as follows: (a) Unified Agents: We define a heterogeneous low-level multi-agent set consisting of |I| vehicle agents for UL and an edge server controller for DL. Specifically, the UL agent set is defined as AUL = {Vi | i ∈ I}, where each vehicle agent Vi determines the UL traffic splitting ratios and transmit (k) power allocation over its associated MBS set Bi . To remain consistent with Problems 1 and 2, the DL decisions are made by the edge server agent, denoted by ADL = {V0 }, which determines the DL traffic splitting ratios from the associated MBSs to the vehicles. Therefore, the overall agent set is A = AUL ∪ADL . Meanwhile, a high-level planner ΠSAGE is further introduced for training-time semantic supervision. (b) Local Observations: For the vehicle agent Vi , the local observation under Problem τ ∈ {1, 2} during the kth DT update is defined as h iT (k,τ ) (k,τ ) UL DL oi = {γi,b }b∈B(k) , {b γb,i }b∈B(k) , zi , Pimax , (38)

(c) Global States: During centralized training, the centralized critic observes the global state during the kth DT update as h i (k,τ ) (k,τ ) s(k,τ ) = {oi }i∈I , o0 , u(k,τ ) , (40)

(k,τ ) where zi denotes the problem-dependent latency state. For (k,1) Problem 1, zi includes the compressed shared backbone UL(k) DL(k) transmission states such as Ξi and Ξi . For Problem (k,2) 2, zi includes the service-aware traffic states such as (k) (k) {λi,q , Wi,q }q∈Q and the corresponding path-latency statistics.

UL where ρ̂UL−split ∈ [0, 1] and ρ̂UL−pwr = P̂i,b /Pimax ∈ [0, 1] i,b i,b are the guided UL traffic splitting tendency and UL power allocation tendency, respectively. The direct prompt action guidance for the edge server V0 is

i

where u(k,τ ) (t) denotes the task-level latency summary. For Problem 1, it corresponds to the round-level joint UL and DL shared-backbone transmission latency; for Problem 2, it corresponds to the service-aware joint UL and DL latency statistics under the kth reconstructed DT. (d) SAGE Planner and Environment Translator: To integrate semantic reasoning into the unified MARL framework, the global state is
first translated into a compact prompt P(k,τ ) = T s(k,τ ) , where T (·) denotes the environment translator. The SAGE planner
then outputs the semantic guidance G(k,τ ) = ΠSAGE P(k,τ ) . For Problem 1, the direct prompted action guidance for vehicle agent Vi is defined as (k,1)

gi

n oT = ρ̂UL−split , ρ̂UL−pwr i,b i,b

(k)

,

(43)

b∈Bi

i

For the DL controller V0 , the local observation is defined as h iT (k,τ ) (k,τ ) DL DL bb,i o0 = {b γb,i }i∈I, b∈B(k) , {R }i∈I, b∈B(k) , z0 , (39) i

i

(k,τ ) where z0 collects problem-dependent global DL states at

V0 , i.e., DL shared-backbone sizes for Problem 1 or serviceaware DL traffic states for Problem 2.

(k,1)

g0

n o = ρ̂DL−split b,i

(k)

.

(44)

i∈I, b∈Bi

For Problem 2, the guidance is extended to the service-aware case. The vehicle agent Vi receives (k,2)

gi

n o UL−split UL−pwr = α̂i,b,q , ρ̂i,b

(k)

b∈Bi

, , q∈Q

(45)

where ρi,b (t) is the UL traffic splitting ratio and Pi,b (t) is the UL transmit power. The edge-server agent controls the DL shared backbone’s transmission: n o (k,1) DL(k) a0 (t) = ρb,i (t) . (48) (k)

the latency reward weight. The second term Ψ(k,τ ) is the high latency penalty using the quadratic function that is against the actions whose resulting latency exceeds the latency budget for both problems, while λvio > 0 is the latency-violation penalty factor. The third term Ωk,τ is the semantic-alignment reward that measures the average consistency between the SAGE guidance and the actual low-level execution across all agents. The dynamic alignment value λsem ≥ 0 becomes insignificant when the learned policies become more consistent with the planned (k,1) strategy. As a result, the reward RSAGE-L (t) for Problem 1 is instantiated as Eq. (41), where the corresponding SAGE action guidance and the actual low-level action execution are defined in Eq. (43)-(44), and Eq. (47)-(48), respectively. Similarly, for (k,2) Problem 2, the reward RSAGE-L (m) is instantiated as Eq. (42), where the corresponding SAGE action guidance and the actual low-level action execution are defined in Eq. (45)-(46) and Eq. (49)-(50), respectively. In addition, αL > 0 in Eq. (41) and Eq. (42) is the scaling parameter.

For Problem 2, the traffic splitting action is further extended to each service type q ∈ Q. The vehicle-agent action becomes n o n o UL(k) (k,2) UL(k) , ∪ P (m) ai (m) = αi,b,q (m) i,b (k) (k)

Remark 2. When λsem = 0, the reward in Eq. (51) reduces to a purely latency-driven reward with a latency-violation penalty, and the proposed SAGE-MAPPO framework generalizes a standard latency-oriented MAPPO design as a special case.

where the UL traffic splitting guidance is service-dependent, while the UL power guidance remains link-dependent. The edge-server guidance is n o (k,2) DL−split . (46) g0 = α̂b,i,q (k) i∈I, b∈Bi

, q∈Q

(e) Actions: To keep the unified SAGE-MAPPO architecture consistent with Problems 1 and 2, we define problemdependent action spaces with the same agent roles. For Problem 1, each vehicle agent Vi controls the UL shared backbone’s transmission over its associated MBSs: n o (k,1) UL(k) UL(k) ai (t) = ρi,b (t), Pi,b (t) , (47) (k) b∈Bi

UL(k)

UL(k)

i∈I, b∈Bi

b∈Bi

, q∈Q

b∈Bi

(49) UL(k) where αi,b,q (m) is the service-aware UL traffic splitting ratio UL(k) and Pi,b (m) is the link-level UL transmit power. The edgeserver action is n o (k,2) DL(k) a0 (m) = αb,i,q (m) . (50) (k) i∈I, b∈Bi

, q∈Q

(f) Unified Latency-driven Reward: We propose a unified reward function by maintaining a single SAGE-MAPPO architecture across the two optimization problems: (k,τ )

RSAGE-L = ϕL Φ(k,τ ) − λvio Ψ(k,τ ) + λsem Ω(k,τ ) ,

(51)

where the designed reward includes three components. The first term Φ(k,τ ) is the exponential latency reward that encourages to minimize the E2E latency in Problems 1 or 2, while ϕL > 0 is (k,1)

(k,1)

RSAGE-L (t) = ϕL · exp −αL · | λsem

maxi∈I Li Lmax(1) {z

Low Latency Reward

(t)

! − λvio · }

|

2) Training Procedure of Unified SAGE-MAPPO: To handle partial observability and temporal dynamics, each agent employs a lightweight encoder and a recurrent policy network. For agent a ∈ A, the local observation is first mapped to (k,τ ) (k,τ ) = fenc(oa ; ϑenc ), and then fed a compact feature ea into a Gated Recurrent Unit (GRU) to update the hidden (k,τ ) (k,τ ) (k,τ ) = GRU(ha , ea ). The decision feature is state ha (k,τ ) (k,τ ) (k,τ ) = [ea , ha ]. For each vehicle agent, the thus za actor network is factorized into an UL traffic splitting head (k,τ ) (k,τ ) (k,τ ) and an UL power control head: πi (ai | zi ) = UL−split UL−pwr πi · πi , while the edge server controller adopts (k,τ ) (k,τ ) (k,τ ) a traffic splitting policy π0 (a0 | z0 ) = π0DL−split . At each decision step, the centralized state is translated into a semantic prompt, and the SAGE planner outputs the guid-

1 X 1 (k,1) · |I| i∈I {Li (t)>Lmax(1) } {z

(k,1)

Li

High Latency Penalty

(t) − Lmax(1) Lmax(1)

!2 + }

     o (41) 1 X X n UL−split DL−split exp −|ρUL−pwr (t) − ρ̂UL−pwr (t)| + exp −|ρUL (t)| + exp −|ρDL (t)| . i,b (t) − ρ̂i,b b,i (t) − ρ̂b,i i,b i,b |I| i∈I (k) b∈Bi

{z

|  (k,2) RSAGE-L (m) = ϕL · exp −αL ·

| λsem |

}

Semantic-Alignment Reward

  2 (k,2) (k,2) max(2) Li,q (m) − Lq 1 X X Li,q (m)  1 XX n o   + − λvio · 1 (k,2) · max(2) max(2) |I| i∈I q∈Q Lmax(2) |I| i∈I q∈Q Li,q (m)>Lq Lq q {z } | {z }

Low Latency Reward

High Latency Penalty

 1 X X  |I| i∈I

(k)

b∈Bi

   Xh    i UL−pwr UL−pwr UL−split DL−split UL DL exp −|ρi,b (m) − ρ̂i,b (m)| + exp −|αi,b,q (m) − α̂i,b,q (m)| + exp −|αb,i,q (m) − α̂b,i,q (m)| .   q∈Q

{z

}

Semantic-Alignment Reward

(42)

Algorithm 3: Unified SAGE-MAPPO for Problems 1 and 2 Input: DT update set K = {0, . . . , K − 1}, environment context τ ∈ {1, 2}, vehicle agent set AUL = {Vi |i ∈ I}, edge server controller V0 , training episodes M , decision steps Tτ , rollout length Lroll , PPO update epochs KPPO (k,τ ) Output: Trained unified policies {πi }i∈I and (k,τ ) π0 Initialize vehicle agent actors {πi }i∈I , edge-server actor π0 , centralized critic, SAGE planner ΠSAGE , translator T (·), and rollout buffer D ← ∅; for each DT update k = 1, . . . , K − 1 do for problem τ = 1, 2 do if τ = 2 then Warm-start the Problem 2 policies using the policy parameters learned from Problem 1 under the current DT update k; for episode e = 1, . . . , M do Reset the problem-τ environment; Obtain initial state s(k,τ ) (0) and (k,τ ) (k,τ ) observations {oi (0)}i∈I , o0 (0); for step n = 0, . . . , Tτ − 1 do Generate semantic guidance
G(k,τ ) (n) = ΠSAGE T (s(k,τ ) (n)) ; for each vehicle agent Vi ∈ AUL do (k,τ ) Encode oi (n) and sample (k,τ ) (k,τ ) ai (n) from πi ; (k,τ )

(k,τ )

Encode o0 (n) and sample a0 (n) (k,τ ) from π0 ; Project all sampled actions onto the feasible region of Problem τ ; Observe s(k,τ ) (n + 1) and compute (k,τ ) RSAGE-L (n) using Eq. (41) if τ = 1, or Eq. (42) if τ = 2; Store the transition in D; if |D| ≥ Lroll then Update all actors and centralized critic using the clipped MAPPO objective with KPPO epochs; Clear D; (k,τ )

}i∈I and

(k,τ )

}k∈K,τ ∈{1,2}

Store the trained policies {πi (k,τ ) π0 ; (k,τ )

return {πi

}i∈I,k∈K,τ ∈{1,2} , {π0

ance G(k,τ ) . The agents then sample their actions from the current policies, interact with the environment, and receive the problem-dependent reward defined in Eq. (41)-(42). The rollout trajectories are stored in an on-policy buffer and used to update the actor and critic networks via the standard clipped MAPPO objective. In Algorithm 3, the generic step index n corresponds to the communication round t for Problem 1 and the transmission block m for Problem 2.

TABLE I: CPFL Hyperparameter Settings Parameter

Configuration

Input feature dimension Shared backbone

5 Env channels + relative distance features MLP 102→256→1024→512, SiLU + LayerNorm Linear 512→ K, dropout = 0.25 MLP 512→384→129, dropout = 0.12 Xavier uniform AdamW 2.6 × 10−4 /1.4 × 2.6 × 10−4 /1.7 × 2.6 × 10−4 128 Huber loss, δ ≈ 0.57 Norm threshold = 1.88 1200 3 Top-37% sparsification + 8-bit quantization

PL task head KPI task head Initialization Optimizer Learning rate (backbone/PL head/KPI head) Batch size Loss function Gradient clip Communication rounds T Local epochs E Gradient compression

TABLE II: Unified SAGE-MAPPO Hyperparameter Settings Parameter

Configuration

Shared actor backbone Critic network Recurrent module Discount factor GAE parameter PPO clipping threshold PPO update epochs Actor learning rate Critic learning rate LLM checkpoint Quantization Inference backend Context length Maximum output tokens Temperature Top-p Sampling top-k Repetition penalty LLM random seed GPU-offloaded layers Output format LLM invocation interval Caching Deployment-time LLM calls

MLP 6 → 128 → 128 → 64, ReLU MLP 73 → 128 → 128 → 64 → 1, ReLU GRU hidden-state update γ = 0.99 λ = 0.95 ϵ = 0.2 K=8 3.0 × 10−4 1.0 × 10−3 Qwen3.5-9B GGUF Q4 K M llama-cpp-python 4096 tokens 384 0.2 0.95 40 1.1 42 20 JSON object Every 1 training episode Disabled 0

IV. P ERFORMANCE E VALUATION This section evaluates the proposed closed-loop framework from two perspectives. First, we verify the effectiveness of the CPFL-enabled V2I DT reconstruction method, including the geometry-aware environmental representation, multi-task weight sensitivity, and PL/KPI prediction accuracy. Second, we evaluate how the reconstructed V2I DT supports the dualstage E2E latency optimization, including DT-assisted V2I association, joint UL and DL transmission latency optimization control via the unified SAGE-MAPPO framework. Experiments4 were conducted in PyTorch with an NVIDIA RTX 4070 GPU. The detailed CPFL and SAGE-MAPPO hyperparameter settings are summarized in Tables I and II, respectively. For the DT reconstruction task, we compare the proposed CPFL-based PFL-MTL method with three representative FL baselines: FedAvg-MTL [38], FedFly [39], and FedGBDT [40]. FedAvg-MTL denotes standard federated MTL without personalized heads. FedFly represents a communication-efficient FL baseline, while FedGBDT denotes a personalized FL method based on gradient boosting. The 4 The simulation code for all experiments in this work can be found at https://github.com/nihaoeveryone404/anonymous-v2i-dt.

TABLE IV: PL and KPI Prediction Performance Comparison. 1.0

Base Stations

BS 17 BS 18 BS 19 BS 20 BS 21 BS 22 BS 23 BS 24 BS 25 BS 26 BS 27 BS 28 BS 29 BS 30 BS 31 BS 32

Scen.

Task

Strategy

RMSE

MAE

Lowload

PL PL PL PL KPI KPI KPI KPI

FedAvg-MTL FedFly FedGBDT Ours FedAvg-MTL FedFly FedGBDT Ours

5.5909 4.2153 4.8912 3.0682 0.0403 0.0298 0.0351 0.0214

4.8641 3.5408 4.3042 2.6079 0.0334 0.0253 0.0305 0.0181

Midload

PL PL PL PL KPI KPI KPI KPI

FedAvg-MTL FedFly FedGBDT Ours FedAvg-MTL FedFly FedGBDT Ours

6.3648 5.8231 6.1045 5.5909 0.0371 0.0234 0.0318 0.0151

5.6010 5.0661 5.3109 4.6963 0.0315 0.0198 0.0273 0.0125

0.8 0.6

LOS score

BS 13 BS 31BS 20 BS 2 BS 12 BS 8 BS 15 BS 14 BS 6BS 29 BS 17 BS 22 BS 3 BS 4BS 9BS 1 BS BS 16 25 BS 24 BS 32 BS 30 BS 21BS 27 BS 10 BS 7 BS 19 BS 18BS 28 BS 23 BS 5 BS 26 BS 11

BS 1 BS 2 BS 3 BS 4 BS 5 BS 6 BS 7 BS 8 BS 9 BS 10 BS 11 BS 12 BS 13 BS 14 BS 15 BS 16

0.4 0.2 0.0

(a) MBS Deployment

(b) LoS Confidence Map

Fig. 3: Overview of the Physical Environment Representations. TABLE III: Performance with Different Multi-Task Weight α. Scenario

Metric

α=0.2

α=0.3

α=0.4

α=0.5

α=0.6

Low-load

PL (RMSE) KPI (RMSE)

7.21 0.078

6.83 0.062

5.89 0.044

5.72 0.042

6.01 0.048

Mid-load

PL (RMSE) KPI (RMSE)

8.12 0.069

7.58 0.057

6.57 0.041

6.51 0.039

6.83 0.043

High-load

PL (RMSE) KPI (RMSE)

9.35 0.086

8.76 0.073

7.90 0.052

7.98 0.051

8.32 0.057

All

PL (RMSE) KPI (RMSE)

6.78 0.054

6.35 0.045

5.48 0.029

5.36 0.022

5.68 0.028

proposed method adopts a shared backbone with personalized PL/KPI heads and compressed shared backbone’s transmission. The joint sparsification and quantization function Q in Eq. (18) employs ps = 37% and nq = 8. For the V2I association and E2E latency optimization task, we compare three baseline strategies. Baseline 1 connects each vehicle to the strongest-SINR MBS: ( 1, b = arg maxb′ ∈Bc γbDL ′ ,i , (B1) (52) wi,b = 0, otherwise, while baseline 2 adopts a rate-proportional soft association strategy: α (Vi,b ) (B2) wi,b = P (53) α. b′ ∈Bi (Vi,b ) The proposed strategy further incorporates the CPFL-predicted KPI-aware utility and LoS confidence to construct a DTassisted soft multi-MBS association, which is then used by the unified LLM-MARL controller for dual E2E latency optimization. A. Performance of V2I DT Reconstruction Fig. 3 illustrates the physical environment representation used by the CPFL-enabled V2I DT. Fig. 3(a) shows the deployment of MBSs over the road network, while Fig. 3(b) presents the reconstructed LoS-confidence map. The LoS map provides a geometry-aware visibility prior, which helps distinguish stable LoS links from deeply blocked NLoS links. Therefore, the proposed DT is not merely a data-driven PL/KPI predictor; it also embeds physically meaningful blockage and visibility information into the subsequent association and latencyoptimization stages. Table III reports the sensitivity of the multi-task weight α. Across Low-, Mid-, High-, and All-load scenarios, the best PL/KPI trade-off consistently appears around α ∈ [0.4, 0.5].

Scen.

Task

Strategy

RMSE

MAE

Highload

PL PL PL PL KPI KPI KPI KPI

FedAvg-MTL FedFly FedGBDT Ours FedAvg-MTL FedFly FedGBDT Ours

7.8508 4.9321 6.5412 3.0860 0.0486 0.0275 0.0392 0.0181

6.9087 4.2909 5.6254 2.5922 0.0422 0.0233 0.0337 0.0150

All

PL PL PL PL KPI KPI KPI KPI

FedAvg-MTL FedFly FedGBDT Ours FedAvg-MTL FedFly FedGBDT Ours

5.2073 3.8451 4.5120 3.0023 0.0192 0.0105 0.0153 0.0063

4.4782 3.2298 3.9254 2.5519 0.0163 0.0089 0.0131 0.0051

For example, in the All-load scenario, the PL Root Mean Square Error (RMSE) decreases from 6.78 at α = 0.1 to 5.36 at α = 0.5, while the KPI RMSE decreases from 0.054 to 0.022. Similar trends can be observed in the other load regimes. This demonstrates that KPI supervision acts as an effective regularizer for PL learning. When α is too small, the model over-emphasizes KPI fitting and weakens the geometric representation required for accurate PL reconstruction. When α is too large, the model becomes overly PL-oriented and loses sensitivity to service-related KPI dynamics. Based on this observation, we adopt α⋆ = 0.45 in the final implementation, which lies near the robust Pareto-optimal region. We further compare the PL and KPI prediction performance of different FL schemes, which is shown in Table IV. The proposed method achieves the lowest RMSE and MAE for both PL and KPI prediction in almost all scenarios. These results verify that the shared backbone can capture common propagation and traffic patterns, while the personalized heads effectively absorb vehicle- and environment-specific Non-IID characteristics. Compared with FedFly and FedGBDT, the proposed method also shows clear advantages. FedFly improves communication efficiency, but its shared representation is less effective in modeling heterogeneous PL/KPI structures. FedGBDT introduces personalization, but its prediction accuracy is still limited in the coupled PL and KPI reconstruction task. In contrast, the proposed CPFL framework benefits from personalized local heads, multi-task supervision, and compressed shared backbone’s transmission. B. Performance of Closed-Loop V2I DT-Assisted Dual E2E Latency Optimization As Fig. 4 shows, we visualize the V2I association behavior under different strategies. Baseline 1 produces rigid serving regions because each vehicle is associated with the strongestSINR MBS. This rule can overload a few strong MBSs and generate severe queueing hotspots. Baseline 2 softens the association through utility-proportional weighting, but it still lacks explicit geometric awareness. In contrast, the proposed method generates more adaptive serving regions by jointly exploiting the CPFL-predicted KPI-aware utility and LoS confidence. The zoomed regions further show that the proposed association strategy can adjust boundaries around intersections, blocked road segments, and transition regions, thereby improving robustness against blockage and load imbalance. Fig. 5 further compares the spatial distributions of DL throughput, average queueing delay, and QoE. In the throughput heatmap, the

Zoom

Baseline 1 BS1 BS2 BS9 BS10 BS17 BS18 BS25 BS26 Zoom

BS1 BS9 BS17 BS25

1st BS BS2 BS10 BS18 BS26

Zoom

BS3 BS11 BS19 BS27

Baseline 2 BS4 BS5 BS12 BS13 BS20 BS21 BS28 BS29

Zoom

BS6 BS14 BS22 BS30

Ours (1st BS) BS7 BS8 BS15 BS16 BS23 BS24 BS31 BS32

(a) V2I Association Topology Zoom

BS3 BS11 BS19 BS27

2nd BS BS4 BS5 BS12 BS13 BS20 BS21 BS28 BS29

(a) Problem 1

(b) Problem 2

Fig. 6: Reward Comparison.

Zoom

3rd BS BS7 BS15 BS23 BS31

BS6 BS14 BS22 BS30

BS8 BS16 BS24 BS32

(b) V2I Association Topology (Ours)

(a) Problem 1

(b) Problem 2

Fig. 7: The CDF Comparison of E2E joint UL and DL Latency.

Fig. 4: DT-Assisted V2I Association Visualization. experience.

Fig. 5: V2I Association Performance Comparison.

We then evaluate the joint UL and DL latency performance of the proposed unified SAGE-MAPPO framework for both problems. Fig. 6 compares the reward evolution of the proposed method with the accelerated MARL approach in Ref. [41] and standard MAPPO for both problems within the first updated DT. In Fig. 6(a), the proposed unified SAGEMAPPO rapidly increases the reward and reaches a stable high-reward region much earlier than the two baselines, which shows its effectiveness in learning the joint UL and DL shared backbone transmission policy for Problem 1. The approach in Ref. [41] also improves the convergence speed over standard MAPPO, but still requires more communication rounds to approach the same reward level. Standard MAPPO converges the slowest and exhibits more pronounced fluctuations due to inefficient exploration in the coupled traffic splitting and power control space. A similar trend is observed in Fig. 6(b) for Problem 2. The proposed method quickly converges within the early training blocks and maintains stable performance afterwards, indicating that the same SAGE-MAPPO architecture can be effectively adapted from CPFL parameter transmission optimization to service-aware E2E latency optimization. The convergence advantage comes from the LLM-based semantic guidance and the shared policy structure between the two problems, which together reduce redundant exploration and provide a warm start across the two optimization stages.

proposed method fills more low-throughput road segments and expands the high-rate service region. In the queueingdelay heatmap, baseline 1 exhibits obvious congestion hotspots, while our proposed method significantly suppresses high-delay regions by distributing traffic across multiple MBSs. In the QoE heatmap, the proposed method produces a broader highQoE serving region, confirming that the throughput improvement and delay reduction are jointly translated into better user

Meanwhile, Fig. 7 presents the E2E latency Cumulative Distribution Function (CDF) comparison for both problems. For Problem 1, Fig. 7(a) shows that the proposed unified SAGEMAPPO with compressed shared backbone’s transmission achieves the left-most CDF curve, indicating the lowest CPFL parameter transmission latency. Compared with path-selection and single-path schemes, the proposed method reduces both median and tail latency by jointly optimizing UL traffic split-

20 Mbps

15 10 5

Baseline 1

Baseline 2

Ours

(a) Downlink Throughput Heatmap

10

6 4

seconds

8

2

Baseline 1

Baseline 2

Ours

(b) Average Queuing Delay Heatmap 5 0 a.u.

5 10 15 20

Baseline 1

Baseline 2

Ours

25

(c) QoE Heatmap

ting, UL transmit power, and DL traffic splitting over multiple MBS paths. The clear gap between the compressed and original schemes further confirms that shared backbone’s compression effectively reduces model transmission latency. For Problem 2, Fig. 7(b) shows that the proposed unified SAGE-MAPPO also shifts the service-level latency CDFs to the left for both service types. This demonstrates that the proposed controller improves average and tail E2E latency by balancing multi-MBS traffic splitting and UL power allocation. In contrast, the single-path baseline suffers from larger latency because it cannot exploit path diversity and is more vulnerable to congested or weak links. Overall, Fig. 7 verifies that the proposed framework reduces both CPFL shared backbone’s transmission latency and service-aware E2E latency.

worst-vehicle E2E joint UL and DL latency of compressed shared backbone exchange during DT reconstruction, whereas Problem 2 minimizes the aggregate service-aware E2E joint UL and DL latency after the reconstructed DT is available. The two problems are operationally decoupled through their execution stages and timescales, while their aligned agent roles and control structures enable cross-problem policy reuse. To solve them efficiently, we developed a unified SAGEMAPPO framework, in which the LLM acts as a trainingtime semantic planner to reduce inefficient exploration, while MARL agents execute feasible low-level actions. Simulation results demonstrate the improved PL/KPI prediction accuracy, more effective DT-assisted V2I association, reduced median and tail latency, and faster convergence than the considered MARL baselines. Future work will investigate online validation using real-world mobility traces, robustness against imperfect DT predictions and semantic guidance, and adaptive DT-update scheduling. A PPENDIX A. Proof of Lemma 1

(b) Problem 1

(a) Problem 2

Fig. 8: Convergence Trend in terms of DT Update Index. We further analyze the convergence of the unified SAGEMAPPO framework from a closed-loop DT-update perspective. As shown in Fig. 8, we compare the number of communication rounds required for convergence in Problem 1 and the number of blocks required for convergence in Problem 2 under different DT update indices. For Problem 1, the unified SAGE-MAPPO converges within far fewer communication rounds than SAGEMAPPO trained only for Problem 1, the accelerated MARL approach in Ref. [41], and standard MAPPO [42]. For Problem 2, a similar trend can be observed: the unified SAGEMAPPO requires fewer convergence blocks than the problemspecific SAGE-MAPPO, the approach in Ref. [41], and standard MAPPO [42]. This confirms that the unified architecture benefits not only from LLM-guided semantic supervision, but also from cross-problem policy reuse. The convergence gain comes from the fact that Problem 1 and Problem 2 share the same agent roles and action structure, i.e., vehicle-side UL traffic splitting and power control together with server/MBSside DL traffic splitting. This closed-loop training mechanism reduces redundant exploration and accelerates convergence compared with training two independent MARL architectures. V. C ONCLUSION In this paper, we proposed a closed-loop dual-stage E2E latency optimization framework for DT-assisted 6G V2I systems. A CPFL-enabled decision-oriented DT was developed to jointly reconstruct PL and KPI-related states while retaining raw vehicle measurements and personalized heads locally. Within each DT update cycle, two distinct but temporally coupled problems were formulated: Problem 1 minimizes the

Proof. According to Assumption 1, let x = xt,e i , t,e+1 t,e and y = xt,e+1 and thus x − x = i i i t,e
−ηw gi,w (xt,e ), −η g (x ) . Then we have v i,v i i h i D E t,e t,e t,e t,e+1 t,e E fi (xt,e+1 ) | x ≤ f (x ) + ∇f (x ), x − x i i i i i i i i 2 L t,e+1 xi − xt,e i 2 t,e t,e = fi (xt,e i ) − ηw ∇w fi (xi ), gi,w (xi )

+

t,e − ηv ∇v fi (xt,e i ), gi,v (xi ) L 2 t,e 2
2 2 η ∥gi,w (xt,e . + i )∥ + ηv ∥gi,v (xi )∥ 2 w (54) According to Assumption  2, we have E[gi,w ] = ∇w fi , E[gi,v ] = ∇v fi , E ∥gi,w − ∇w fi ∥2 ≤ σ 2 , and 2 E∥gi,v − ∇v fi ∥2 ≤ σ 2. As E ∥g∥ = ∥E[g]∥2 +  2 2 E ∥g − E[g]∥ , we ≤ ∥∇w fi (x)∥2 +σ 2  obtain E ∥gi,w (x)∥ 2 2 2 and E ∥gi,v (x)∥h ≤ ∥∇v fi (x)∥ i + σ . Taking the total

in terms of xt,e expectation of E fi (xt,e+1 ) | xt,e i i i , we obtain

 


2 L 2 fi xt,e+1 ≤ fi xt,e − ηw − ηw ∇w fi xt,e i i i 2  
2 L 2
L − ηv − ηv2 ∇v fi xt,e + ηw + ηv2 σ 2 . i 2 2 (55) 2 Let the step sizes satisfy ηw , ηv ≤ L1 , then ηw − L2 ηw ≥ η2w and ηv − L2 ηv2 ≥ η2v . Then Eq. (55) can be written as

1 t,e 2 fi (xt,e+1 ) ≤ fi (xt,e i i ) − (ηw ∥∇w fi (xi )∥ 2
L 2 2 + ηv ∥∇v fi (xt,e η + ηv2 σ 2 . i )∥ ) + 2 w

(56)

B. Proof of Lemma 2 Proof. For the communication round t, the local drift for vehicle i at step e is wit,e+1 = wit,e − ηw gi,w . Thus the

local drift for E steps within a whole round is wit,e+1 = PE−1 wit,e − ηw e=0 gi,w . Then 2 2 wit,E − wt = ηw

E−1 X

2 ≤ ηw E

2 ≤ ηw E

2 e gi,w

e=0 E−1 X e=0 E−1 X

e gi,w

2

(57)

∥∇w fi (x)∥2 + σ 2 .

e=0

According to Assumption 4, we have |I| h
2i
2i 1 X h t,e + γ2. ≤ E ∇ F x E ∇w fi xt,e w i |I| i=1 (58) Therefore, according to Eq. (57) and Eq. (58), we have |I| i
1 X h t,E 2 2 E wi − w t ≤ C ηw E 2 σ2 + γ 2 . |I| i=1

(59)

C. Proof of Theorem 1 Proof. FromPcommunication round t to t + 1 with E steps, t,E 1 wt+1 = |I| and vit+1 = vit,E . Then i wi   fi (wt+1 , vit,E ) − fi (wt , vit ) = fi (wit,E , vit,E ) − fi (wt , vit )   + fi (wt+1 , vit,E ) − fi (wit,E , vit,E ) . (60)

Thus we have F t+1 − F t =

1 X t,0  fi (xt,E i ) − fi (xi ) |I| i {z } | A

 1 X + fi (wt+1 , vit,E ) − fi (wit,E , vit,E ) . |I| i | {z }

(61)

#   1 X t+1 t,E t,E t,E ,w − wi ⟩ E(B) ≤ E ⟨∇w fi wi , vi |I| i # " 2 L 1 X + E wt+1 − wit,E 2 |I| i # "  2  ηw 1 X t,E t,E ≤ E f i wi , v i 4 |I| i #   " 2 1 L 1 X + + wit,E − wt+1 E ηw 2 |I| i # " E−1 i 2 ηw X h 1 X t+1 t 2 t,E ≤ E ∇w F + CLE wi − w 4 e=0 |I| i # " i 2 ηw E h 1 X t t 2 t,E ≤ . + CLE E ∇w F wi − w 4 |I| i (64) "

c Let ηw ≤ LE . According to Lemma 2, combine Eq. (61)-(64), we have i     ηw E h 2 E ∇w F t E F t+1 ≤ E F t − # "4 E−1 ηv X 1 X t,e
2 (65) ∇ v fi xi − E 4 e=0 |I| i
2 2 + C1 LE ηw + ηv2 σ 2 + C2 Lηw E2γ2.

Summing Eq. (65) from t = 0 to T − 1, we obtain T −1 i ηw E X h 2 E ∇w F t 4 t=0 " # T −1 E−1 ηv X X 1 X t,e
2 + E ∇v f i x i 4 t=0 e=0 |I| i
2 2 − T (C1 LE ηw + ηv2 σ 2 + C2 Lηw E 2 γ 2 ). (66) Under Assumption 3, we further obtain

E[F 0 ] − E[F T ] ≥

T −1

According to Lemma 1, summing over e = 0, . . . , E − 1 and averaging over vehicles i, we obtain # " E−1 ηw X 1 X t,e
2 E ∇ w f i xi E(A) ≤ − 2 e=0 |I| i " # E−1
ηv X 1 X LE 2 t,e
2 − E ∇v fi xi ηw + ηv2 σ 2 . + 2 e=0 |I| i 2 (62)

Under Assumption 1, in terms of the shared backbone w, we have     fi wt+1 , vit,E ≤ fi wit,E , vit,E D   E + ∇w fi wit,E , vit,E , wt+1 − wit,E 2 L wt+1 − wit,E , 2

t,E and vit+1 = vit,E . While i wi

P

0

i 4 F −F 1 X h 2 E ∇w F t ≤ T t=0 ηw ET

B

+

where wt+1 = N1

(63)

⋆

+ C1 Lηw σ 2 + C2 Lηw Eγ 2 , (67)

and  
|I| T −1 E−1
4 F0 − F⋆ 1 XX  1 X 2 t,e ≤ E ∇vi fi xi T E t=0 e=0 |I| i=1 ηv T E +

4 2 2 (C1 LE ηw + ηv2 σ 2 + C2 Lηw E 2 γ 2 ). ηv E

(68) Combining the two bounds in Eq. (67) and Eq. (68) and rearranging them in terms of Gt yields the main theorem. R EFERENCES [1] S. Aboagye, M. Amin Saeidi, H. Tabassum, Y. Tayyar, E. Hossain, H.-C. Yang, and M.-S. Alouini, “Multi-band wireless communication networks: Fundamentals, challenges, and resource allocation,” IEEE Transactions on Communications, vol. 72, no. 7, pp. 4333–4383, 2024. [2] B. Hu, J. Du, J. Zhang, and X. Chu, “Computation offloading and resource allocation in mixed cloud/vehicular-fog computing systems,” IEEE Transactions on Mobile Computing, vol. 24, no. 9, pp. 8612–8624, 2025.

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